How to model the wavy wrapper of a cupcake?
Well, here's how I would model "the thing that cupcakes are in":

Start with a cylinder with an even number of vertices (like 40) and NGon cap fill:



Give the cylinder the shape of a cupcake

Select the top face and make it larger by scaling it (S). Then, delete the face (X):



Select half of the side edges


Switch to edge selecting mode
Select one edge at the top and one at the bottom circles
Multi select loops (Press Space and search for this function)
Select inverse (ControlI)
Checker deselect (again, search for this)




Create the waves

Make this selection larger by scaling it:



If you don't like the spikes, scale down in the z-direction (S to scale, and Z to use the z axis.



Fix the bottom

Go back to face selection mode and select the bottom face. Scale down over the z-axis to make the face flat. Then, poke it (AltP). This will split the face into triangles, which is better for rendering.



Make it look nicer

Exit edit mode (Tab). Add the Solidify modifier. Adjust the thickness as desired. Add the Bevel modifier, with a very small width (like 0.02). Add the Subdivision surface modifier, to smooth it out. You can play with the settings a bit, and you should get something like this: